In [1]} the Cauchy problem related to a very general model of nonlocal continuum mechanics, inspired
by the seminal work by S.A. Silling (see [2]}), was studied and the analytical aspects concerning global solutions in energy space were exploited in the framework of nonlinear hyperelastic constitutive assumptions.
More precisely, the governing equation of the motion of an infinite
body is modeled in [1]}
by the initial-value problem
\({\left\lbrace \begin{array}{ll}\partial _{tt} \mathbf {u}(\mathbf {x},t)=(K\mathbf {u}(\cdot ,t))(\mathbf {x}),&\quad \mathbf {x}\in \mathbb {R}^N,\: t >0,\\\mathbf {u}(\mathbf {x},0)=\mathbf {u}_0(\mathbf {x}),\:\partial _t \mathbf {u}(\mathbf {x},0)=\mathbf {v}_0(\mathbf {x}),&\quad \mathbf {x}\in \mathbb {R}^N,\end{array}\right.}\) 
